# Lesson 2From Polygons to CirclesSolidify Understanding

Calculate the perimeter and area for each figure.

perimeter:

area:

### 2.

perimeter of green (both inside and outside):

area of green:

perimeter:

area:

perimeter:

area:

perimeter:

area:

perimeter:

area:

## Set

### 7.

A circle and several congruent squares with side lengths equal to the radius of the circle are shown. Use these squares to estimate how many squares it takes to fill in the area of the circle. State what you notice. (Try using tracing paper or create cutouts to make a good estimate.)

### 8.

Which polygon has an area and perimeter closest to the circle in which it is inscribed? Why?

### 9.

Given that the radius of each circle in the previous problem is feet, find the area of each of the regular polygons inscribed in the circle. List each area in the table below, along with the measure of one angle for each polygon and the side length of each polygon. (One interior angle and one side length are given.)

Shape

One Interior Angle

Length of One Side

Area of Figure

Triangle

Square

Pentagon

Hexagon

Octagon

Decagon

Circle

### 10.

Explain how a circle can be cut into sectors and reconfigured to appear approximately as a polygon that could have its area calculated using a standard formula. (Use a diagram with your explanation.)

### 11.

Explain how a circle can be broken into several rings or interior circles that can be rearranged to appear approximately as a polygon that could have its area calculated using a standard formula. (Use a diagram with your explanation.)

## Go

Use the given circle in the following problems to find the indicated measures:

1. circumference of the entire circle

2. the fractional part of the circle represented by the ratio of the central angle to

3. the shortest arc length that is intercepted by the central angle

(The shortest arc length from to is called the minor arc. The long distance from to around the circle is called the major arc.)

### 12.

1. circumference of circle:

2. ratio of central angle to :

3. the shortest arc length :

### 13.

1. circumference of circle:

2. ratio of central angle to :

3. the shortest arc length :

### 14.

1. circumference of circle:

2. ratio of central angle to :

3. the shortest arc length :

### 15.

1. circumference of circle:

2. ratio of central angle to :

3. the shortest arc length :